An intended ground track of an aircraft may be calculated as a geodesic curve (or simply as a geodesic) that is a path with the shortest distance between two locations on the surface of a given earth model. The length of the geodesic curve is measured along the surface of the given earth model, as is defined for the ground track of an aircraft. A two-dimensional (sometimes referred to as “2D” or “2-D”) geodesic is a straight line.
Regulatory documents have contemplated mandates that geodesic curves are to be based on an ellipsoidal earth model that is defined by the World Geodetic System 84 (WGS-84) coordinate system, instead of a spherical earth model that is currently used by some flight management system (FMS) products.
The Federal Aviation Administration's (FAA's) Next Generation Air Transportation Modernization (sometimes referred to as “NextGen”) program and the Single European Sky Air Traffic Management (ATM) Research (SESAR) program require a four-dimensional (sometimes referred to as “4D” or “4-D”; e.g., three spatial dimensions and a time dimension) trajectory architecture. Under the NextGen and SESAR programs, a flight management systems (FMS) would need to generate the 4-D trajectory of the aircraft and coordinate with the flight control system to track the 4-D trajectory within required positioning and timing thresholds. Such programs require that the FMS precisely defines an aircraft's intended ground track on the surface of the World Geodetic System 84 (WGS-84) ellipsoidal earth model.
The computation of geodesics and bearings on the surface of an ellipsoidal model involves differential geometry, which is mathematically and computationally complex. While geodetic algorithms exist that can be used to accurately compute the bearing of a geodesic curve and construct the ground track of an aircraft on the surface of the WGS-84 ellipsoidal earth model, such geodetic algorithms require a high computational load. Additionally, constructing the ground track of an aircraft by utilizing such geodesic algorithms would require the design, development, testing, and certification of new software to work with existing aviation equipment.